I have a RB750G and once in a while it hangs on me and I cant get to it at night and users get really mad. What is the best approach I can take to even power cycle it remotely. Any solution/idea is welcome.

The best approach would be to use the logs to figure out why it hangs up in the first place. It shouldn't. Figuring out how to reboot it when it hangs up is equivalent to slapping a band aid on it. Fixing it would ensure you don't need a band aid.

Well concerning the logs is it possible to save logs and retrieve then after rebooting since once I reboot it they disappear. One of the reason am asking for such a solution is because it has just happened twice in 6 months and it happens at the wrong time and the downtime could be solved by a reboot as I figure out what went wrong in the first place.

You could use the remote logging facility if you have a server that runs syslog.
You might also get some relief by setting up the system watchdog timer.

Lastly you can install a ping rebooter in the box. There are a number of them out there to do that job. They generally cost more than the routerboard, but certainly less than the problem can cost you. I have a couple such devices in use in my network in troubled places where we cant seem to find the real issue. It is a band aid, but if its only happening every couple months, your customers probably wont notice the reboot outage.

When it hangs, does the power go away or does the router stop responding?
Also have you noticed if the lights on the ethernet ports still blink or do they stop?

It should be possible to create a small circuit that will interrupt power for 10 seconds when it detects no activity
for so many minutes.
Just an idea.

When it hangs, does the power go away or does the router stop responding?
Also have you noticed if the lights on the ethernet ports still blink or do they stop?

It should be possible to create a small circuit that will interrupt power for 10 seconds when it detects no activity
for so many minutes.
Just an idea.

The router is usually in a remote location so I never looked at the lights. I would be interested in such a circuit.
There was one time when the router was authenticating users and passing traffic but I couldn't ssh or access it via web. I had to power cycle it the following day.

you could setup netwatch to ping a closer ip address, and if it fails it reboots

Also, concerning the logging, you could set it to also log to disk. This way you can easily pull the file straight off the router to inspect it once you get it up and running again.